{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:X557ID4INUKDUEZ7SLWXMRSRPZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a602537fa2332740f491abbdad761b05603206838c84881be7ceb8057d968904","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-14T19:32:37Z","title_canon_sha256":"6e8bbe1548ce2507f96c81052bc962a6e16868b7b82508a2c3ad1c7ec4ea3b46"},"schema_version":"1.0","source":{"id":"1310.3802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3802","created_at":"2026-05-18T03:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3802v1","created_at":"2026-05-18T03:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3802","created_at":"2026-05-18T03:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"X557ID4INUKD","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"X557ID4INUKDUEZ7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"X557ID4I","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:9b4f34ef1fe194da10f0e9edabcff048d6fbb1716d3b0033d7aaa579e1e370f0","target":"graph","created_at":"2026-05-18T03:10:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper is devoted to the study of equidistributional properties of \\textit{totient points} in $\\mathbb{N}^r$, that is, of coprime $r$-tuples of integers, with particular emphasis on some relevant sets of totient points fulfilling extra divisibility or coprimality conditions, or lying on arithmetic progressions.","authors_text":"Jos\\'e L. Fern\\'andez, Pablo Fern\\'andez","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-14T19:32:37Z","title":"Equidistribution and coprimality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3802","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9d216e1f8aaddcccb493b2e28b4e4a8d0acac36ceb7e89cfef290137b0957b3d","target":"record","created_at":"2026-05-18T03:10:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a602537fa2332740f491abbdad761b05603206838c84881be7ceb8057d968904","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-14T19:32:37Z","title_canon_sha256":"6e8bbe1548ce2507f96c81052bc962a6e16868b7b82508a2c3ad1c7ec4ea3b46"},"schema_version":"1.0","source":{"id":"1310.3802","kind":"arxiv","version":1}},"canonical_sha256":"bf7bf40f886d143a133f92ed7646517e5423dff4aa0d4fecc8be1bbba4a583fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf7bf40f886d143a133f92ed7646517e5423dff4aa0d4fecc8be1bbba4a583fe","first_computed_at":"2026-05-18T03:10:34.867336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:34.867336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5jyKP5tqnFp92kXMJcCb1H8t8esed27/1dpZYmdOzWcJCiPpwCDp3PozSumF3yJzQyYqe32f3K6phYImA5eZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:34.867942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d216e1f8aaddcccb493b2e28b4e4a8d0acac36ceb7e89cfef290137b0957b3d","sha256:9b4f34ef1fe194da10f0e9edabcff048d6fbb1716d3b0033d7aaa579e1e370f0"],"state_sha256":"7c6b0b698a51b2e331118692199ff4e1cceb415940f94382718d0f9d5e348143"}